Let's solve each binary number and convert it to its hexadecimal equivalent step by step.
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🔹 Step-by-Step Conversion Process:
To convert
binary to
hexadecimal, follow these steps:
1.
Group the binary digits into sets of 4, starting from the right (least significant bit).
2. If the leftmost group has fewer than 4 bits,
pad with zeros on the left.
3. Convert each 4-bit group to its
hexadecimal equivalent using the table below.
| Binary | Hex |
|--------|-----|
| 0000 | 0 |
| 0001 | 1 |
| 0010 | 2 |
| 0011 | 3 |
| 0100 | 4 |
| 0101 | 5 |
| 0110 | 6 |
| 0111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | A |
| 1011 | B |
| 1100 | C |
| 1101 | D |
| 1110 | E |
| 1111 | F |
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Now let’s go through each problem.
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1) 111011₂
- Group into 4s: `0011 1011` (add two leading zeros)
- `0011` = 3
- `1011` = B
-
✔ Answer: 3B₁₆
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2) 11000111₂
- Group: `1100 0111`
- `1100` = C
- `0111` = 7
-
✔ Answer: C7₁₆
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3) 10010010₂
- Group: `1001 0010`
- `1001` = 9
- `0010` = 2
-
✔ Answer: 92₁₆
---
4) 10111101₂
- Group: `1011 1101`
- `1011` = B
- `1101` = D
-
✔ Answer: BD₁₆
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5) 1001110₂
- Add leading zero to make 4-bit groups: `0100 1110`
- `0100` = 4
- `1110` = E
-
✔ Answer: 4E₁₆
---
6) 11010110₂
- Group: `1101 0110`
- `1101` = D
- `0110` = 6
-
✔ Answer: D6₁₆
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7) 11111111₂
- Group: `1111 1111`
- `1111` = F
- `1111` = F
-
✔ Answer: FF₁₆
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8) 110100101₂
- This has 9 bits → pad to make groups of 4:
- `0001 1010 0101` (added 3 zeros at the start)
- `0001` = 1
- `1010` = A
- `0101` = 5
-
✔ Answer: 1A5₁₆
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9) 100010000₂
- Total bits: 9 → pad to make groups:
- `0001 0001 0000`
- `0001` = 1
- `0001` = 1
- `0000` = 0
-
✔ Answer: 110₁₆
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10) 11000₂
- Only 5 bits → pad to make groups:
- `0110 00` → add one zero → `0001 1000`
- `0001` = 1
- `1000` = 8
-
✔ Answer: 18₁₆
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✔ Final Answers:
1)
3B₁₆
2)
C7₁₆
3)
92₁₆
4)
BD₁₆
5)
4E₁₆
6)
D6₁₆
7)
FF₁₆
8)
1A5₁₆
9)
110₁₆
10)
18₁₆
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Let me know if you'd like this as a printable answer key or need explanations in another format!
Parent Tip: Review the logic above to help your child master the concept of decimal to binary worksheet.
